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Cambridge International Examinations
Cambridge International General Certificate of Secondary Education
MATHEMATICS
0580/02
For Examination from 2015
Paper 2 (Extended)
SPECIMEN MARK SCHEME
1 hour 30 minutes
MAXIMUM MARK: 70
The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level 1/Level 2 Certificate.
This document consists of 4 printed pages.
© UCLES 2012
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2
Types of mark
M marks are given for a correct method.
A marks are given for an accurate answer following a correct method.
B marks are given for a correct statement or step.
D marks are given for a clear and appropriately accurate drawing.
P marks are given for accurate plotting of points.
E marks are given for correctly explaining or establishing a given result.
SC marks are given for special cases that are worthy of some credit.
Abbreviations
cao
correct answer only
cso
correct solution only
dep
dependent
ft
follow through after error
isw
ignore subsequent working
oe
or equivalent
SC
Special Case
www
without wrong working
art
anything rounding to
soi
seen or implied
Qu.
Answers
1
7.5(0) cao
2
Mark
Part Marks
258.75
4.6
2
M1 for
3 × 1027
2
M1 for 6 ÷ (2 × 10–27)
3
cos38 sin38 sin158 cos158
2
M1 correct decimals seen
0.7(88..) 0.6(15..) 0.3(74..) –0.9(271..)
4
41
333
5
(a) 7853 to 7855
or 7850 or 7860 www
(b) 0.7853 to 0.7855 or 0.785 or 0.786
3
2
1ft
6
135 cao
3
7
(a) (y =) 80
1
(b) (z =) 40
1
(c) (t =) 10
1ft
© UCLES 2012
0580/02/SM/15
123
oe fraction
999
or M1 for 1000[x] = 123.123… oe
B2 for
M1 for π × 502
Their (a) ÷ 10 000 evaluated
M1 for 720 or (6 – 2) × 180 oe seen in working
and M1 for equation 180 + 4x = their 720
or
M1 for (360 − 180) ÷ 4 (= 45) oe seen in
working
and M1 dep for 180 − their 45
Follow through 90 − their y or 50 − their z
3
8
y= −
1
x +10 oe
2
3
M2 for −
1
x + 10
2
or M1 for gradient identified as −
1
2
or intercept as 10 (not on diagram)
e.g. y = mx + 10 or
1
y= − x+c
2
9
10
11
12
(a) Correct perpendicular bisector with
arcs
2
(b) 60°
1
4
B1 0.8, 0.6 or 0.55 then
M1 0.45 × their 0.6 M1 0.2 × their 0.55
or M2 1 – (0.45 × 0.4 + 0.55 × their 0.8)
 8 5

(a) 
 20 13 
2
B1 two or three entries correct
 1 1 − 12 
 oe
(b)  2
− 2 1 
2
 3 − 1
1 a c 
 B1 (k )

B1 
2 b d 
− 4 2 
(a) Negative
1
Ignore embellishments
(b) Correct point
1
(c) (i)
1
0.38 or
19
50
Accurate ruled line
(ii) English mark
13
B1 correct line
B1 correct construction arcs
(a)
1
1
a + b oe
2
2
1ft
2
Follow through their (c)(i)
M1 unsimplified or any correct route
e.g a +
1
1
(b) –1 a + 1 b oe
2
2
2
1
(b – a) or OA + AC
2
M1 unsimplified or any correct route
e.g. CD = 1
14
(a) 2.84
2
M1 correct substitution of g and ℓ seen
3
M1 each correct move but third move marked on
answer line
(a) 156
4
M1 intention to find area under graph
B2 completely correct area statement
or B1 two areas found correctly (or one
trapezium area)
(b) 12
1ft
(b)
15
1
1
AB or b – a + (b – a)
2
2
© UCLES 2012
4π 2 l
oe
T2
0580/02/SM/15
Their (a)/13
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4
16
(a) 500, 405, 364–365, 295 (…)
2
B2
(b) 5 points plotted within correct square
1
P1 ft from table
1
C1
1
B1 ft from their curve or line reading at 350 g
correct curve drawn within 1 mm of
points plotted
(c) (i) 3.3–3.4
17
(ii) Never oe
1
1
2
2
B1 f(–2) seen
2
M1 x –1 = y3 or 3√(y – 1)
(c) 1 2
3
M2 (x – 1)(x – 2) = 0
or M1 (x + a)(x + b) = 0 where
ab = 2 or a + b = –3
If 0 scored give M1 for x2 – 3x + 2 = 0
(a) 4324 cao
2
M1
(b) (i)
2
B1 either correct
(a)
(b) 3√(x – 1) or
18
(c)
© UCLES 2012
3
x −1
4, 9
(ii) (n + 1)2 or n2 + 2n + 1
1
2
n(n+ 1)(2n + 1) oe
3
2
0580/02/SM/15
1
× 23 × 24 × 47 or better
6
M1 recognising Vn = 4Tn